Measurement and control of in-plane surface chemistryduring the oxidation of H-terminated (111) SiBilal Gokcea, Eric J. Adlesa,b, David E. Aspnesa,1, and Kenan Gundogdua,1

aPhysics Department, North Carolina State University, Raleigh, NC 27695; and bApplied Physics Laboratory, Johns Hopkins University, Laurel, MD 20723

Contributed by David E. Aspnes, August 10, 2010 (sent for review July 7, 2010)

In-plane directional control of surface chemistry during interfaceformation can lead to new opportunities regarding device struc-tures and applications. Control of this type requires techniques thatcan probe and hence provide feedback on the chemical reactivity ofbonds not only in specific directions but also in real time. Here, wedemonstrate both control and measurement of the oxidation ofH-terminated (111) Si. Control is achieved by externally applyinguniaxial strain, and measurement by second-harmonic generation(SHG) together with the anisotropic-bond model of nonlinear op-tics. In this system anisotropy results because bonds in the straindirection oxidize faster than those perpendicular to it, leading inaddition to transient structural changes that can also be detectedat the bond level by SHG.

silicon ∣ hyperpolarizability ∣ ellipsometry ∣ metrology ∣ optical

The oxidation of silicon is one of the most technologically im-portant chemical reactions. Because dangling bonds trap and/or scatter carriers, well-organized bonding at Si∕SiO2 interfaces iscritical to device performance. Therefore, although Si oxidationhas been studied for many years, the formation dynamics ofSi∕SiO2 interfaces continues to be of interest. The informationprovided to date regarding oxidation kinetics has been obtainedprimarily by standard spectroscopic and microscopic structural-analysis techniques. For example, scanning tunneling microscopyand atomic force microscopy (AFM) studies have revealed therole of surface morphology during oxidation (1, 2). IR absorptionexperiments have probed the changes in vibrational modes duringoxidation and have provided information about the chemicalreactions involved in the process (3). Spectroscopic ellipsometryhas provided data about growth rates (4). At the same time, con-siderable effort has been invested in manipulating Si oxidationkinetics. For example, uni- and biaxial strains have been usedin manufacturing Si-based devices, taking advantage of the factthat tensile stress increases the overall oxidation rate of thermallygrown oxides (5).

The effect of strain on the morphology of clean vicinal andon-axis Si surfaces has been well studied by microscopic methods(6, 7). However, an atomic-level understanding of the specificeffects of strain on surface chemistry is presently unknown. Here,we investigate oxidation of strained and unstrained H-terminated(111) Si in real time using second-harmonic generation (SHG),and we analyze these data with the anisotropic-bond model(ABM) of nonlinear optics. The bond-specific information thatwe obtain reveals two important aspects of the relevant chemicaldynamics. First, strain changes the oxidation rates of Si─Si backbonds that are oriented in different directions, and second, theaverage back-bond directions themselves change as a result ofthis anisotropic oxidation.

Fig. 1 provides an atomic-level view of the configuration, show-ing the bonding of the outermost bilayer of a (111) Si surface.Each outer-layer Si atom has one “up” bond, here initially termi-nated by H, and three “back” bonds to underlying Si atoms. Uponair exposure oxidation occurs, with H being replaced by O or OH,and O inserting itself into Si─Si bonds. In SHG an incomingbeam at a frequency ω (red) is converted into an outgoing beam

at a frequency 2ω (blue) in a way that allows us to follow sepa-rately the up and back bonds, as described below.

Under standard conditions in air the oxidation of H-termi-nated (111) Si is purely statistical, with no preferred orientation.That is, all three sets of back bonds oxidize at the same averagerate. However, we find that the application of an external uniaxialstress increases the reactivity of the bonds most nearly alignedwith the stress direction. This means that we can select specificSi─Si back bonds to oxidize faster than others. This indicates thepossibility of in-plane control of chemistry during oxide growthand paves the way for previously undescribed opportunities toengineer interfaces for device applications.

Our results also show that local structural changes andassociated microscopic strains are secondary consequences ofO insertion into Si─Si back bonds. These changes cannot be ob-served in the oxidation of unstrained on-axis samples because themacroscopic symmetry remains C3v, so the changes average tozero. However, in strained material the bonds reorient collec-tively, resulting in easily detected changes in the observed azi-muth angles of the bonds in the SHG-anisotropy (SHGA)data. This has further implications for the determination of struc-tural dynamics. These are conventionally measured by X-ray orelectron diffraction, which are techniques that are sensitivemainly to nuclear locations. By showing that structural dynamicscan be probed directly from the bonds that actually establishatomic structure, we obtain information that is more direct. Ourresults show that nonlinear optics can be used for this purpose.

Fig. 1. Atomic-level illustration of surface bonds of (111)Si.

Author contributions: E.J.A., D.E.A., and K.G. designed research; B.G. and E.J.A. performedresearch; B.G. and K.G. analyzed data; and B.G., D.E.A., and K.G. wrote the paper.

The authors declare no conflict of interest.

Data deposition: The data reported in this paper have been deposited at http://www.physics.ncsu.edu/gundogdu/pnas2010.html.1To whom correspondence may be addressed. E-mail: aspnes@ncsu.edu orkenan_gundogdu@ncsu.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1011295107/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1011295107 PNAS ∣ October 12, 2010 ∣ vol. 107 ∣ no. 41 ∣ 17503–17508

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http://www.physics.ncsu.edu/gundogdu/pnas2010.htmlhttp://www.physics.ncsu.edu/gundogdu/pnas2010.htmlhttp://www.physics.ncsu.edu/gundogdu/pnas2010.htmlhttp://www.physics.ncsu.edu/gundogdu/pnas2010.htmlhttp://www.physics.ncsu.edu/gundogdu/pnas2010.htmlhttp://www.physics.ncsu.edu/gundogdu/pnas2010.htmlhttp://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1011295107/-/DCSupplementalhttp://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1011295107/-/DCSupplementalhttp://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1011295107/-/DCSupplementalhttp://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1011295107/-/DCSupplementalhttp://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1011295107/-/DCSupplementalhttp://www.pnas.org/lookup/suppl/doi:10.1073/pnas.1011295107/-/DCSupplemental

Results and DiscussionIn-Plane Control of Oxidation Chemistry. SHGA data of a singular(111) Si surface are shown in Fig. 2. The black points were ob-tained from a sample terminated with a natural oxide, and the redpoints for an H-terminated sample as quickly as possible aftertreatment. According to the bond model, the major features inthe oxidized-surface data occur when one of the h1-1-1i,h-11-1i, and h-1-11i back bonds is nearly parallel to the drivingfield. For p-polarized light incident at 45°, this minimum angleis 8.4°, and it occurs when the bond is in the plane of incidencepointing approximately toward the illumination direction. Thethree smaller peaks are rectified versions of negative field extre-ma, which are made positive because the intensity, being propor-tional to the square of the field, is positive definite. For theH-terminated surface the major peaks are much smaller andthe major and minor peaks are reversed, reflecting partly the re-duced electronegativity of H and a relative enhancement of thecontribution of the (isotropic) top bond in this case.

Figure 3 shows the results of consecutive SHGA scans for threeH-terminated singular (111) Si samples during air oxidation. Inall the cases the signal starts with the SHG response of theH-terminated surface, as shown as the red points in Fig. 2. It thenincreases to a maximum before decreasing to the reference levelfor the oxidized surface, shown as the black points in Fig. 2. How-ever, the SHGA responses differ significantly during oxidation.Fig. 2A shows data for the unstrained sample. Here, the threemajor peaks evolve similarly during oxidation, indicating thatoxidation is proceeding isotropically on the macroscopic scale.Fig. 2 B and C display similar data obtained for strain appliedalong the h-12-1i and h-101i directions, respectively. The peaksevolve at different rates for the strained samples.

For the data of Fig. 3B, the h-12-1i direction of the applied0.13% strain aligns most closely with the direction of theh-11-1i bond. The angles between the strain direction and thebonds are specifically 19.5° for the h-11-1i bond and 61.9° forthe other two. This is consistent with the increased reactivityof the h-11-1i bond as seen in the data, indicating that strainhas the greatest influence on the chemical reactivity of bondsin the strain direction, which is probably not surprising. Thealternative case is shown in Fig. 3C. Here, the 0.08% strain alongh-101i is perpendicular to the h-11-1i bonds and therefore mainlyaffects the chemical reactivity in the other two bond directions. In

this case the middle peak rises more slowly. For both experimentsinvolving strain, the SHG response starts and ends with C3v sym-metry, indicating that the states of the initial and final surfacesare alike. The observed differences are therefore due to thechemical processes involved while oxidation is occurring.

Modeling the SHGA Data.To relate the SHGA data to the oxidationof bonds in the different directions, we first need to establish theevolution of oxide thickness. To do this we performed SE mea-surements under the ambient conditions described above. Datafor an unstrained surface are shown in Fig. 4 A and B. These wereobtained at a photon energy of 2.83 eV to maximize the distinc-tion between oxide and interfacial layer, as discussed in Materialsand Methods. To avoid artifacts due to hydrocarbon contamina-tion, the surfaces were rinsed in methanol prior to each datum.We repeated the measurements for strained surfaces at differenttimes after H termination. Surprisingly, the oxide and interfacethicknesses for all surfaces are the same to within the experimen-

Fig. 2. SHGA response of oxidized (black dots) and H-terminated (red dots)(111)Si for p-polarized excitation and detection. In both cases the data for theunstrained surface exhibit C3v symmetry. (Inset) Bonding of a surface-layeratom of a (111)-oriented Si crystal, looking down from the top. A peak inthe oxidized-surface response occurs whenever one of the back bonds alignsnearly parallel to the excitation field.

Fig. 3. Evolution of SHGA p-p data for three initially H-terminated (111)Sisamples during air exposure. Red arrows (Insets) mark the direction of thestrain applied to the silicon crystal from the bond perspective. (A) no appliedstrain; (B) 0.13% external strain applied along h-12-1i; (C) 0.08% externalstrain applied along h-101i.

Fig. 4. Thicknesses for an on-axis surface as determined by SE (A) for theoxide and (B) for the interface layers.

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tal uncertainty of �1 Å. Thus the average SiO2 overlayer thick-ness evolves at essentially the same rate for strained and un-strained surfaces, regardless of the relatively complicatedkinetics revealed by SHGA.

However, we can gain further information from the compar-ison. For all cases the maximum SHGA amplitudes are observedwhen the oxide layer is 2 to 4 Å thick, which corresponds tooxidation of the first Si bilayer. When the SHG data reach theirequilibrium levels, the thickness is about 6 Å. For later times C3vsymmetry recovers, but the oxide thickness continues to increaseuntil saturating near 8 Å. Therefore, for the strain levels involvedin these experiments, the observed anisotropic behavior of theoxidation kinetics is related to the oxidation of the topmost Sibilayer. The anisotropy does not persist for lower layers.

We obtain the evolution of the hyperpolarizabilities of thefour bond directions by fitting Eq. 2 to the SHGA responses.The results are given in Fig. 5. Because oxidation occurs at dif-ferent times for bonds in a given direction, at any given time theseare average polarizabilities. Nevertheless, the picture yields goodinsight into the reaction kinetics of individual bonds.

The relationship between the chemical nature of a bond andits hyperpolarizability is subtle. When a bond undergoes a che-mical change, the electronic potential is primarily altered at thebond, but the potentials of neighboring bonds are affected as well.However, some general conclusions can still be drawn. Consider-ing the rise of the SHGA response for the first 60 to 80 min for allsamples, as shown in Fig. 5, the striking results are (i) the signifi-cant change in the average hyperpolarizability of the up bondsand (ii) the near balance between this hyperpolarizbility andthose of the back bonds. The magnitudes of all four hyperpolar-izabilities increase with oxidation, which is exactly what we expectfrom the differences in electronegativity between O and H. Thenear balance can be understood as a consequence of chemicalinduction. The capping atoms draw charge from the capped Siatom in proportion to their electronegativities, thus also modify-ing the hyperpolarizabilities of the back bonds in proportion tothe adsorbate electronegativities. Because the contribution of theup bonds is independent of sample azimuth, it would be difficultto extract it directly from the raw SHGA data of Fig. 3 withoutmodeling.

During the rising part of the SHGA signal some back bondsalso oxidize. That is, the increase in SHGA signal and the averagehyperpolarizabilities shown in Fig. 5 are not due solely to oxida-

tion of the up bonds. We gather this from two observations. First,the SE data indicate that the oxide thickness is about 2 to 4 Å at80 min. This exceeds the value expected for a single monolayer ofOH capping the top silicon atoms. Second, the hyperpolarizabil-ities of the back bonds of the strained surfaces are themselvesanisotropic, which suggests differences in their average chemicalnature. However, this effect is much smaller than that seen in theup bonds. The back-bond hyperpolarizabilities increase only by afactor of 3, in comparison with the 60-fold increase in that of theup bonds.

The reason for this smaller change is evident when we considerthe nature of the bonding. The oxidation of the top bonds createsan obviously asymmetric potential. However, oxidation of theback bonds replaces a Si─Si bond with a Si─O─Si combination,which is somewhat symmetric. If both Si atoms were the same andthe bond linear, then the SHGA response of the configurationwould vanish. However, the terminating Si atoms differ from eachother by their electronegativities. Because O insertion forms aSi─O─Si bridge and introduces microscopic strain, the Si bondsinvolved will be deflected from the directions that they wouldhave in the ideal crystal lattice. Therefore, the excitation fieldis expected to better align with only one of Si─O bonds in anSi─O─Si bridge, increasing the SHG efficiency. Neverthelessthe net hyperpolarizabilities of the oxidized back bonds can neverbecome as strong as that of up bonds.

Consistent with previous IR studies (3), the above discussionindicates a two-step oxidation process. First, the observed chemi-cal change in the up bonds is most likely a replacement of H withOH. Second, O insertion occurs in the Si─Si bilayer. To lowestorder we would expect uniaxial strain to affect the reactivity ofback bonds more than that of the up bonds.

To obtain a more quantitative understanding of reaction ratesfor the different bond directions, we attempted to fit the hyper-polarizabilities to exponential functions. However, simple expo-nentials gave very poor fits, with large errors. Thus it is clear thatthe reaction rates of the up and back bonds are coupled. Whileoxidation may initiate with the up bonds, back-bond oxidationbegins soon afterward and introduces local strain, which furthercomplicates oxidation kinetics. Therefore, the rate parametersare not constant, but change as oxidation proceeds. Processes likethis are well known in biology, where intertwined factors contri-bute to population changes. Such processes can be described bythe Chapman–Richards equation (8)

Fig. 5. Evolution of the average hyperpolarizabilities for all Si bonds from the data shown in Fig. 3. These values are obtained by fitting the SHGA response tothe function given by Eq. 2. The green lines show fits to the Chapman–Richards function given in Eq. 1. The specific hyperpolarizabilities are (A) up bond of theunstrained sample; (B) up bond of the sample strained along h-12-1i; (C) up bond of the sample strained along h-101i; (D) back bonds of the unstrained sample;(E) back bonds of the sample strained along h-12-1i; (F) back bonds of the sample strained along h-101i.

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W ðtÞ ¼ Uð1 − e−ctÞn þ y0: [1]

The results of fitting to this equation are the green curves of Fig. 5.The fit during the initial part of the data up through the maxima isexcellent. The resulting parameters are summarized in Table 1.

The actual relationship between these parameters and thechemical reactivity of particular bonds requires theoretical calcu-lations of the hyperpolarizabilities of expected configurations.This can certainly be done, but is beyond the scope of this article.However, our results emphasize the complexity of these chemicalprocesses at the bond level and also show that these complexitiescan be revealed by a combination of nonlinear optics and aniso-tropic-bond modeling.

Real-Time Control of Surface Chemistry. We now investigate thepossibility of using strain to manipulate oxidation kinetics in realtime. Fig. 6 shows data for an on-axis (111) surface similar tothose shown above. For the first 10 min no strain is applied tothe sample. During this interval the SHGA evolution is consistentwith C3v symmetry. At 10 min we applied strain along an arbitrarydirection. C3v symmetry is immediately broken, with peaks corre-sponding to different bond directions now oxidizing at differentrates. As with our previous experiments, the SHGA responseeventually develops C3v symmetry, as expected for an on-axissample. These data occur at a substantially later time and conse-quently are not shown in Fig. 6.

Effect of Steps on Oxidation Kinetics. The above data show thatstrain plays a significant role in the oxidation kinetics ofH-terminated (111) Si surfaces. Because steps can also modifyoxidation kinetics, we need to investigate step effects as well.Consequently, we performed control experiments on vicinal(111) Si wafers offcut ð4.6� 0.1Þ° toward [11-2]. These surfacesconsist of two distinct regions: steps and terraces. The terraceshave the local structure of the on-axis samples. The steps havea dangling bond in the h11-1i direction and a support bond alongh-1-1-1i.

Real-time SHGA data for one of these vicinal samples areshown in Fig. 7. Six features are apparent. Three grow to approxi-mately the same amplitude, then decay. However, the oxidationkinetics is significantly different from that of strained orunstrained on-axis samples. The early oxidation dynamics ishighlighted in Fig. 7B, which shows the SHGA scans for the first5 min together with those at 20 and 25 min. For the first 20 minwe see little activity, and at the earliest times the h-1-11i featureis missing. After 25 min the amplitudes of the major featuresincrease at a faster rate, and all reach their maximum valuesapproximately 75 min into oxidation.

The differences between on-axis and vicinal surfaces allow usto draw two conclusions. First, the anisotropic oxidation that weobserve for the on-axis samples is not due to inadvertent arrays ofsteps on the surface. Second, oxidation of vicinal samples shows astrong dependence on steps and therefore exhibits significantlydifferent dynamics with respect to strained and unstrained on-axissurfaces.

The role of steps in the oxidation kinetics of Si surfaces hasbeen the subject of debate. Some reports suggest that oxidationdoes not initiate at step sides (9). However, FTIR data indicatethat steps facilitate oxidation (10). Our data elucidate the crucialrole of steps. In Fig. 8A, we show the results of an ABM simula-tion of the SHGA first scan of Fig. 7B, where the unoxidized stepis shown in Fig. 8B and the oxidized step in Fig. 8C. The modelassumes that the h111i support bonds at the sides of the step oxi-dize first. In this case the SHGA signal arises from one Si─Hstep bond and two Si─Si� back bonds, where Si� represents aSi atom bonded to O. Oxidation of the support bonds actuallyreduces the asymmetry at the Si─H dangling bond, as discussedabove, and increases the asymmetry of the Si─Si� bonds. Themodel successfully reproduces the data, supporting the conclu-sion that for vicinal orientations oxidation indeed starts at thesupport bonds of the steps and, in fact, proceeds fast enoughto have gone to completion by the time the first scan couldbe started. At later times oxidation of terrace bonds dominatesthe SHG response. But with reaction kinetics dominated bysteps, we could not observe any differences in the oxidation ki-netics of strained and unstrained vicinal samples.

Bond-Specific Structural Dynamics. The observed oxidation aniso-tropies of strained surfaces also lead to bond-level structuraldynamics that can be observed in SHGA data. The Si─O bondlength of 1.60 Å is incommensurate with the Si─Si bond length of2.35 Å, so oxidation of particular bonds introduces local micro-scopic strain that is much larger than the macroscopic appliedstrain and hence can cause additional structural changes. To in-vestigate these effects, we determined the azimuth angles of thepeaks of the SHGA data of Fig. 3. The azimuths were extractedby fitting the evolving features with Gaussian functions, althoughother functions could also be used without changing the results.These are shown in Fig. 9 A–C. They were also correlated withmodels created by molecular mechanics 2 (MM2) force-field cal-

Fig. 6. SHGA response for the first 190 min for an initially H-terminated sin-gular (111)Si surface as a function of air exposure. No strain was applied forthe first 10 min. At that time, marked by the black arrow, strain was appliedin an arbitrary direction. (Inset) 3D plot of the same data.

Table 1. Parameters yielding the best fits of Eq. 1 to the data ofFig. 5.

U C n y0

Fig. 5A h111i 30.151 0.063 2.561 0.370Fig. 5B h111i 27.129 0.036 1.452 1.040Fig. 5C h111i 31.592 0.077 2.215 0.366Fig. 5D h-1-11i, h-11-1i, h1-1-1i −0.849 0.072 4.055 −0.496Fig. 5E h-1-11i, h1-1-1i −0.516 0.037 3.950 −0.529Fig. 5E h-11-1i −0.587 0.046 2.873 −0.580Fig. 5F h-11-1i −0.671 0.116 8.001 −0.556Fig. 5F h-1-11i, h1-1-1i −0.752 0.106 5.144 −0.573

Fig. 7. Oxidation of vicinal surface. (A) Evolution of p-p SHGA data for a4.6°-vicinal, initially H-terminated (111)Si sample during air exposure. (B)The first four SHGA scans of the data in A, together with those at 20 and25 min.

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culations, which are shown in Fig. 9 D–F. Because of programlimitations it is not possible to create a silicon lattice with morethan 100 atoms, so the MM2 calculations are not quantitativelyaccurate. Nevertheless, they are sufficient to show trends.

All figures show that the initial and asymptotic azimuths exhi-bit the expected equilibrium values for an unperturbed (111) Silattice. This is also the case of the on-axis sample throughoutoxidation, Fig. 9A, where oxidation is stochastic and the averageazimuthal angle for each bond remains constant to within �0.3°.However, significant discrepancies are seen for different bonds inFig. 9 B and C. In particular, for Fig. 9B, where 0.13% strain is

applied along h-12-1i, the average azimuth-angle decrease of sev-eral degrees shows that the h1-1-1i and h-1-11i bonds move awayfrom each other upon oxidation but before oxidation is com-pleted. This is consistent with the MM2 calculation shown inFig. 9E. When 0.08% strain is applied along h-101i, Fig. 9C showsthat the average azimuth angles increase by several degrees. Thusthe h1-1-1i and h-1-11i bonds both move away from the h-11-1ibond. This is again consistent with the diagram provided inFig. 9F. These azimuthal variations indicate an initial accumula-tion, followed by a relaxation, of microscopic strain. Althoughsuch local strains are necessarily a general consequence of oxida-tion, the fact that macroscopic strain makes oxidation anisotropicallows us to resolve properties of individual types of bonds andhence to observe the effect. These data together with the analysisof the experiment on the strained sample clearly indicate thatSHGA provides a bond sensitive structural characterizationmethod. Oxidation of the vicinal sample is mandated by the stepstructure; hence no structural dynamics are observable.

ConclusionControl of in-plane chemistry by manipulating reaction rates ofcertain bond directions is a unique concept, with potential appli-cations in semiconductor technology. The first important step toachieving such control is the development of bond-specific meth-ods that can characterize these effects. By applying a uniaxialstrain during Si─SiO2 interface formation, we demonstrate thatSHGA provides the route to characterization followed by controlfor Si oxidation. We not only are able to control chemical reac-tivity along different bond directions, but also to probe structuralevolution by measuring changes in bond directions.

Previously, similar nonlinear-optical experiments were mod-eled by tensorial calculations (11–13), which are based on thesymmetry of the underlying Si lattice. However, our data empha-size that chemistry takes place in real time at the atomic scaleand that symmetry is an end result of chemical processes; i.e.,it is not constant but evolves in time. Therefore, effective real-time analysis of nonlinear-optical signals requires models basedon microscopic parameters. The ABM used in this work facili-tates the interpretation of SHGA experiments, expanding itsapplications to surface chemistry. Our approach of using SHG

Fig. 8. Bond model analysis of the initial oxidation of the vicinal surface.(A, blue dots) SHGA data for the first scan in Fig. 7A, together with anABM simulation (black line). The simulation assumes that only the supportbonds at the step sides in B are oxidized, as shown in by the red atoms inC. The hyperpolarizabilities used in the simulation are 2–8i, 0.3, 0.8, and0.8 for the Si─O support bond, the Si─H bond, and the two Si─Si bondsto the terraces, respectively.

Fig. 9. Analysis of bond-specific structural dynamics. (A) Evolution of the azimuths of the dominant features for the unstrained on-axis sample. (B) As A, butfor the sample strained along h-12-1i. (C) As B, but for strain along h-101i. (D–F) Results of force-field calculations showing the result of O insertion in differentbonds.

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to study dynamics is general and can be applied to problems thatrange from bond formation during chemical changes on surfacesto bond dynamics in functional materials that exhibit phase tran-sitions. Although Si might appear to be a special case owing to therelative lack of SHG signals from the bulk, the measurementsdone here depend mainly on differences with respect to an intrin-sic reference and thus become more an issue of precision ratherthan accuracy. We anticipate that significantly more informationwill become available from these measurements once nonlinear-optical spectroscopy becomes routine.

Materials and MethodsSamples. To ensure that the observed phenomena are not specific to growthand processing, we used (111)-oriented Si wafers from three different sup-pliers. Data were obtained on n-type samples of about 5 Ω cm resistivity andtwo different orientations: one at ð0.0� 0.1Þ° and the other at ð4.6� 0.1Þ°toward [11-2], as determined by X-ray diffraction. Samples were cleanedby consecutive 10-min immersions in 80 °C NaOH∕H2O2∕H2O (1∶1∶5) and80 °C HCl∕H2O2∕H2O (1∶1∶5). Native oxides were then stripped and thetop orbitals of the outmost Si atoms capped with H by a 20-min immersionin 40% NH4F. To minimize pitting, the NH4F solutions were deoxygenatedprior to immersion (14). Measurements began approximately 90 s afterthe samples were removed from the NH4F solution and dried with high-purity N2. All measurements were made at room temperature in ambientlaboratory conditions.

Experiments. Second-Harmonic Generation and Spectral Ellipsometry. Experi-mental details are provided at http://www.physics.ncsu.edu/gundogdu/pnas2010.html.

Strain. We placed the front surface of the samples under tension by bendingthem over cylindrical mandrels of specified radii of curvature. The macro-scopic strains themselves were determined by reflection anisotropy measure-ments (15). This geometry also ensured that strain in the perpendicularin-surface direction was negligible.

Theory. Nonlinear-optical data are generally described in terms of tensors,i.e., macroscopic crystal symmetries (16, 17) However, during chemical reac-tions these symmetries break and reform, making tensor-based interpreta-tions challenging. We overcome this difficulty with the anisotropic-bondmodel (18, 19). In this model, when a particular asymmetric bond is alignedparallel to the driving field, the acceleration of its bond charge, and hence itsradiated SHG signal, is maximized. This formulation simply follows the basicphysics of nonlinear optics (NLO), specifically interpreting the NLO response

as the far-field radiation emitted by bond charges driven anharmonicallyalong bond directions. The calculation involves four steps: first, evaluatethe local (driving) field at the charge site; second, solve the force equationto find the resulting motion of the charge; third, calculate the radiationresulting from the acceleration of the charge; and fourth, superpose the ra-diation from all charges. In the present configuration the observed second-harmonic radiation is due to the nonlinear polarization of the individualbonds, with the signal partially cancelled by a relativistic effect (19). Wemakethe simplifying assumption that only motion along the bond axis is relevant,which is equivalent to assuming that the bonds are rotationally symmetric.If desired, macroscopic tensor representations can be calculated directlybecause crystal symmetry is built in at the atomic level.

The above procedure yields the analytic expression for dipolar contribu-tions to SHG (or first-order nonlinearities)

E2ωf f ∝ ∑j

qðb̂j · ~EÞ2b̂j ¼ ∑j

αjb̂j; [2]

where the b̂j are the unit vectors along bond directions and the αj the bondhyperpolarizabilities determined by the electronic potential. Eq. 2 providesthe atomic-scale connection between the observed SHG signal and the inter-face parameters, which we follow in real time to extract the chemicalchanges that occur on a bond-specific basis.

The outermost atoms of the (111) surface of tetrahedrally bonded mate-rials such as Si have one up orbital and three Si─Si back bonds. For H-passi-vated Si the up orbital is capped with H, forming a Si─H bond. On Pauling’sscale the electronegativity of H is 2.20, whereas that of Si is 1.90. Hence allfour outer-layer bonds are asymmetric, the up bonds from the electronega-tivity difference itself, and the back bonds from chemical induction. In thebond model this asymmetry translates into an anharmonicity of the restoringforce acting on the associated bond charge, and thus the efficiency of SHGproduction by the bond. The overall SHG signal nominally also contains anelectric-quadrupole contribution from the bulk, but this is independent ofsurface conditions. Hence the large changes that we observe are due to theinterface. Under ambient laboratory conditions the initial reaction replacesthe H caps with OH−. This is followed by insertion of O into back bonds, withthe O forming bridges between Si atoms. Because the electronegativity of Ois 3.44, oxidation significantly increases bond asymmetry and hence the SHGsignal of the associated bonds. As the Si─O bond length of 1.60 Å is incom-mensurate with the Si─Si bond length of 2.35 Å, oxidation also introduceslocal strain, which in turn affects the reaction kinetics. We detect this not onlyin the oxidation rates themselves, but also as changes in the azimuth anglesof the peaks in the SHGA data as discussed in connection with Fig. 9.

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